Converting decimals into fractions
Objective: Interpret percents as a part of a hundred; find decimal and percent equivalents for common
fractions and explain why they represent the same value; compute a given percent of a whole number.
(5NS 1.2)
Remind students about the names of the
place values to the right of the decimal,
how to verbally express decimals in word
form, and how they are written as
fractions.
Say (Word
Form)
Fraction
0.1
one tenth
1
10
1
101
0.01
one hundredth
1
100
1
10 2
0.001
one
thousandth
1
1000
1
10 3
Decimal
Fraction with
Powers of 10
ASK: “What do you notice about the
number of decimal places and the
denominators in each fraction?”
[The number of decimal places is the
power of 10 in the denominator. i.e.
two decimal places => 10
2
= 100 ]
Example 1: (Model with direct instruction)
Express 0.8 as a fraction in simplest form.
Simplify with Prime
Factorization
Model with Base-10
Blocks
Simplify with Greatest
Common Factor
1
8
10
2i2i2
0.8 =
2i5
4
0.8 =
5
8
10
8 2
0.8 =
÷
10 2
4
0.8 =
5
0.8 =
0.8 =
1
1
GCF = 2
8 4
=
10 5
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Example 2: (Model with direct instruction)
Express 0.08 as a fraction in simplest form.
Simplify with Prime
Factorization
Model with Base-10
Blocks
Simplify with Greatest
Common Factor
1
8
100
2i2i2
0.08 =
2i2i5i5
2
0.08 =
25
8
100
8
4
0.08 =
÷ GCF = 4
100 4
2
0.08 =
25
0.08 =
0.08 =
11
8
2
=
100 25
ASK: What do you notice about the two
different models for 0.8 and 0.08?
[Accept any reasonable responses. Sample:
0.08 is much smaller than 0.8.]
Example 3: (You Try!)
Express 0.5 as a fraction in simplest form.
Simplify with Prime
Factorization
Model with Base-10
Blocks
Simplify with Greatest
Common Factor
1
5
10
5
0.5 =
2i5
1
0.5 =
2
5
10
5 5
0.5 =
÷
10 5
1
0.5 =
2
0.5 =
0.5 =
1
GCF = 5
5 1
=
10 2
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Example 4: (You Try!)
Express 0.28 as a fraction in simplest form.
Simplify with Prime
Factorization
Model with Base-10
Blocks
Simplify with Greatest
Common Factor
1
28
100
2i2i7
0.28 =
2i2i5i5
7
0.28 =
25
28
100
28 4
0.28 =
÷ GCF = 4
100 4
7
0.28 =
25
0.28 =
0.28 =
11
28
7
=
100 25
CST Released Test Questions: (Once students understand the conceptual model, move away from it and use
only as needed to scaffold the concept.)
What is the decimal 0.4 written as a fraction?
What is the decimal 0.48 written as a fraction?
Simplify with Prime
Factorization
Simplify with Prime
Factorization
Simplify with Greatest
Common Factor
GCF = 2
4
10
2i2
0.4 =
2i5
2
0.4 =
5
0.4 =
1
Simplify with Greatest
Common Factor
GCF = 4
48
100
2i2i2i2i3
0.48 =
2i2i5i5
12
0.48 =
25
4
10
4 2
0.4 =
÷
10 2
2
0.4 =
5
0.48 =
0.4 =
11
Page 3 of 6
48
100
48 4
0.48 =
÷
100 4
12
0.48 =
25
0.48 =
MCC@WCCUSD 12/01/11
Converting Fractions to Decimals
When the denominator is a 10, 100, or 1,000:
7
0.7 =
10
81
0.81 =
100
9
0.009 =
1000
407
0.407 =
1000
Therefore:
Remind students that when we
convert decimals to fractions, the
number of decimal places reveals
the value of the denominator. The
same is true when converting
fractions to decimals.
The denominator informs us how
many decimal places our number will
contain. 1000 = 10 3 , therefore our
answer has three (3) decimal places.
8
10
25
100
276
1000
17
10
= 0.8
= 0.25
= 0.276
= 1.7
Making equivalent fractions:
1
2 2 2
= i
5 5 2
4
=
10
= 0.4
2
= 1 , therefore according to the
2
Identity Property of Multiplication the
2
value of remains the same.
5
Other examples:
3
3 2
= i
50 50 2
6
=
100
= 0.06
6
6 4
= i
25 25 4
24
=
100
= 0.24
CST Released Test Question:
What decimal is equal to
A)
B)
C)
D)
0.30
0.35
0.60
1.67
3
?
5
5 5 25
= i
4 4 25
125
=
100
= 1.25
7
7 4
=
i
250 250 4
28
=
1000
= 0.028
Solution:
3 3 20
= i
5 5 20
=
60
100
= 0.60
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Using division:
5
=5÷8
8
So,
0.625
8 5.000
-4 8
20
-16
40
-40
0
The Secret to Dividing with Decimals
Adding zeros after (or to the right) of a
decimal point does not change a
number’s value!
5
= 0.625
8
Other examples:
1
15 3i5
=
9 3i3
=5÷3
So,
15
= 1.66
9
2
1.66
3 5.00
-3
20
-1 8
20
-18
2
2
2
=2+
5
5
= 2 + (2 ÷ 5)
= 2 + 0.4
= 2.4
So, 2
0.4
5 2.0
-2 0
0
2
= 2.4
5
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Converting Decimals and Fractions into
Percents
Decimal-to-percent conversions are made by moving the decimal
point two places to the right.
0.15 = 15%
2.97 = 297%
0.0043 = 0.43%
The Math Behind Moving the Decimal
Per cent means “per hundred” in Latin. So, when
we multiply a number by 100, the decimal moves
two places to the right and we get our percent.
Note: 0.43% is less than 1% and should not be confused
with 43% which is 0.43 as a decimal!
Converting fractions-to-percents is actually a two step process.
First convert the fraction into a decimal, then convert the equivalent
decimal into a percent as demonstrated in the above procedure.
1
=1÷ 4
4
3
= 3÷ 2
2
0.25
4 1.00
- 8
20
-20
0
1
= 0.25 = 25%
4
1.5
2 3.0
-2
10
-10
0
3
= 1.5 = 150%
2
CST Released Test Question:
Solution:
A company donated 200 books to a local
library. If 70 of them were fiction, what
percent of the donated books are fiction?
fiction 70
=
all
200
7i10
=
20i10
7
=
20
= 7 ÷ 20
A)
B)
C)
D)
35%
40%
60%
65%
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0.25i100 = 25
1.5i100 = 150
7
, 0.35=35%.
20
A is the correct
answer.
So,
0.35
20 7.00
-6 0
10
-1 0
0
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